The improper ferroelectricity in ${\mathrm{YMnO}}_3$ and other related multiferroic hexagonal manganites is known to cause topologically protected ferroelectric domains that give rise to rich and diverse physical phenomena. The local structure and structural coherence across the ferroelectric transition, however, were previously not well understood. Here, we reveal the evolution of the local structure with temperature in ${\mathrm{YMnO}}_3$ using neutron total scattering techniques, and we interpret them with the help of first-principles calculations and with a first-principles-based effective Hamiltonian. The results show that, at room temperature, the local and average structures are consistent with the established ferroelectric $P{6}_{3}cm$ symmetry. On heating, both local and average structural analyses show striking anomalies from about 800 K up to the Curie temperature and signatures of a locally more preserved structure than on average, consistent with increasing fluctuations of the order-parameter angle. These fluctuations result in an unusual local symmetry lowering into a continuum of structures on heating. This local symmetry breaking persists into the high-symmetry nonpolar phase, constituting an unconventional type of order-disorder transition, and we pinpoint it as the reason for the anomalous behavior near the phase transition. The hidden disorder revealed in ${\mathrm{YMnO}}_3$ by total scattering is expected to find analogies in other materials with structural frustration or characteristic energy barriers of different magnitudes.

Power laws in nature are considered to be signatures of complexity. The theory of self-organized criticality (SOC) was proposed to explain their origins. A long-standing principle of SOC is the separation of timescales axiom. It dictates that external input is delivered to the system at a much slower rate compared to the timescale of internal dynamics. The statistics of neural avalanches in the brain was demonstrated to follow a power law, indicating closeness to a critical state. Moreover, criticality was shown to be a beneficial state for various computations leading to the hypothesis that the brain is a SOC system. However, for neuronal systems that are constantly bombarded by incoming signals, the separation of timescales assumption is unnatural. Recently, it was experimentally demonstrated that a proper correction of the avalanche detection algorithm to account for the increased drive during task performance leads to a change of the power-law exponent from 1.5 to approximately 1.3, but there is so far no theoretical explanation for this change. Here, we investigate the importance of timescale separation, by partly abandoning it in various models. We achieve it by allowing for an external input during the avalanche, without compromising the separation of avalanches. We develop an analytic treatment and provide numerical simulations of a simple neuronal model. If the input strength scales as one over the network size, we call it a moderate input regime. In this regime, a scale-free behavior is observed; i.e., the avalanche size follows a 1.25 power law, independent of the exact size of the input. For a perfectly timescale separated system, an exponent of 1.5 is observed. Thus, the universality class of the system is changed by the external input, and the change of the exponent is in good agreement with experimental observations from nonhuman primates. We confirm our analytical findings by simulations of the more realistic branching network model.

We propose and analyze a protocol to study quantum information scrambling using statistical correlations between measurements, which are performed after evolving a quantum system from randomized initial states. We prove that the resulting correlations precisely capture the so-called out-of-time-ordered correlators and can be used to probe chaos in strongly interacting, many-body systems. Our protocol requires neither reversing time evolution nor auxiliary degrees of freedom, and it can be realized in state-of-the-art quantum simulation experiments.

The Mpemba effect is a counterintuitive relaxation phenomenon, where a system prepared at a hot temperature cools down faster than an identical system initiated at a cold temperature when both are quenched to an even colder bath. Such nonmonotonic relaxations are observed in various systems, including water, magnetic alloys, polymers, and driven granular gases. We analyze the Mpemba effect in Markovian dynamics and discover that a stronger version of the effect often exists for a carefully chosen set of initial temperatures. In this strong Mpemba effect, the relaxation time jumps to a smaller value leading to exponentially faster equilibration dynamics. The number of such special initial temperatures defines the Mpemba index, whose parity is a topological property of the system. To demonstrate these concepts, we first analyze the different types of Mpemba relaxations in the mean-field antiferromagnetic Ising model, which demonstrates a surprisingly rich Mpemba-phase diagram. Moreover, we show that the strong effect survives the thermodynamic limit and that it is tightly connected with thermal overshoot; in the relaxation process, the temperature of the relaxing system can decay nonmonotonically as a function of time. Using the parity of the Mpemba index, we then study the occurrence of the strong Mpemba effect in a large class of thermal quench processes and show that it happens with nonzero probability even in the thermodynamic limit. This study is done by introducing the isotropic model for which we obtain analytical lower bound estimates for the probability of the strong Mpemba effects. Consequently, we expect that such exponentially faster relaxations can be observed experimentally in a wide variety of systems.

We establish a lower bound on the asymptotic secret key rate of continuous-variable quantum key distribution with a discrete modulation of coherent states. The bound is valid against collective attacks and is obtained by formulating the problem as a semidefinite program. We illustrate our general approach with the quadrature-phase-shift-keying modulation scheme and show that distances over 100 km are achievable for realistic values of noise. We also discuss the application to more complex quadrature-amplitude-modulation schemes. This result opens the way to establishing the full security of continuous-variable protocols with a discrete modulation, and thereby to the large-scale deployment of these protocols for quantum key distribution.

Despite the importance of fluid flow for transporting and organizing populations, few laboratory systems exist to systematically investigate the impact of advection on their spatial evolutionary dynamics. To address this problem, we study the morphology and genetic spatial structure of microbial colonies growing on the surface of a nutrient-laden fluid ${10}^4$ to ${10}^5$ times more viscous than water in Petri dishes; the extreme but finite viscosity inhibits undesired thermal convection and allows populations to effectively live at the air-liquid interface due to capillary forces. We discover that S. cerevisiae (baker’s yeast) growing on a viscous liquid behave like “active matter”: They metabolically generate fluid flows many times larger than their unperturbed colony expansion speed, and that flow, in turn, can dramatically impact their colony morphology and spatial population genetics. We show that yeast cells generate fluid flows by consuming surrounding nutrients and decreasing the local substrate density, leading to misaligned fluid pressure and density contours, which ultimately generates vorticity via a thresholdless baroclinic instability. Numerical simulations with experimentally measured parameters demonstrate that an intense vortex ring is produced below the colony’s edge. As the viscosity of the substrate is lowered and the self-induced flow intensifies, we observe three distinct morphologies: At the highest viscosity, cell proliferation and movement produces compact circular colonies with, however, a stretched regime of exponential expansion; intermediate viscosities give rise to compact colonies with “fingers” that are usually monoclonal and then break into smaller cell clusters; at the lowest viscosity, the expanding colony fractures into many genetically diverse, mutually repelling, islandlike fragments that can colonize an entire 94-mm-diameter Petri dish within 36 hours. We propose a simple phenomenological model that predicts the early colony dynamics. Our results provide rich opportunities to study the interplay between fluid flow and spatial population genetics for future investigations.

Here, we present a fundamental study on how the ground-state chemical reactivity of a single molecule can be modified in a QED scenario, i.e., when it is placed inside a nanoscale cavity and there is strong coupling between the cavity field and vibrational modes within the molecule. We work with a model system for the molecule (Shin-Metiu model) in which nuclear, electronic, and photonic degrees of freedom are treated on the same footing. This simplified model allows the comparison of exact quantum reaction rate calculations with predictions emerging from transition state theory based on the cavity Born-Oppenheimer approach. We demonstrate that QED effects are indeed able to significantly modify activation barriers in chemical reactions and, as a consequence, reaction rates. The critical physical parameter controlling this effect is the permanent dipole of the molecule and how this magnitude changes along the reaction coordinate. We show that the effective coupling can lead to significant single-molecule energy shifts in an experimentally available nanoparticle-on-mirror cavity. We then apply the validated theory to a realistic case (internal rotation in the 1,2-dichloroethane molecule), showing how reactions can be inhibited or catalyzed depending on the profile of the molecular dipole. Furthermore, we discuss the absence of resonance effects in the present scenario, which can be understood through its connection to Casimir-Polder forces. Finally, we treat the case of many-molecule strong coupling and find collective modifications of reaction rates if the molecular permanent dipole moments are oriented with respect to the cavity field.

We resolve phonon number states in the spectrum of a superconducting qubit coupled to a multimode acoustic cavity. Crucial to this resolution is the sharp frequency dependence in the qubit-phonon interaction engineered by coupling the qubit to surface acoustic waves in two locations separated by $\sim 40$ acoustic wavelengths. In analogy to double-slit diffraction, the resulting interference generates high-contrast frequency structure in the qubit-phonon interaction. We observe this frequency structure both in the coupling rate to multiple cavity modes and in the qubit spontaneous emission rate into unconfined modes. We use this sharp frequency structure to resolve single phonons by tuning the qubit to a frequency of destructive interference where all acoustic interactions are dispersive. By exciting several detuned yet strongly coupled phononic modes and measuring the resulting qubit spectrum, we observe that, for two modes, the device enters the strong dispersive regime where single phonons are spectrally resolved.

Unconventional superconductors are often characterized by numerous competing and even intertwined orders in their phase diagrams. The fluctuations associated with these orders may provide the exotic pairing glue that underlies their high-temperature superconductivity. Helimagnet MnP, the first Mn-based superconductor under pressure, lacks high rotational symmetry. However, our resonant soft x-ray scattering experiment discovers novel helical orbital density wave (ODW) orders in MnP and reveals intertwined ordering phenomena. In particular, an ODW forms with half the period of the spin order and fully develops slightly above the spin ordering temperature, which resembles the behaviors of the nematic phase of the iron-based superconductors. Moreover, we find that their domains develop simultaneously, yet the spin order domains are larger than those of the ODW; and they cooperatively produce another ODW with $1/3$ the period of the spin order. These observations provide a comprehensive picture of the intertwined orders in this three-dimensional, low-symmetry system and shed light on the understanding of its superconducting mechanism.

Topological mechanics has been studied intensively in periodic lattices in the past a few years, leading to the discovery of topologically protected boundary floppy modes in Maxwell lattices. In this paper, we extend this concept to two-dimensional quasicrystalline parallelogram tilings, and we use the Penrose tiling as our example to demonstrate that topological boundary floppy modes can arise from a small geometric perturbation to the tiling. The same construction can also be applied to disordered parallelogram tilings to generate topological boundary floppy modes. We find that a topological polarization can be defined for quasicrystalline structures as a bulk topological invariant. Remarkably, due to the unusual orientational symmetry of quasicrystals, the resulting topological polarization can exhibit orientational symmetries not allowed in periodic lattices. We prove the existence of these topological boundary floppy modes using a duality theorem which relates floppy modes and states of self-stress in parallelogram tilings and fiber networks, which are Maxwell reciprocal diagrams to one another. Our result reveals new physics about the interplay between topological states and quasicrystalline order and leads to novel designs of quasicrystalline topological mechanical metamaterials.

Quasiparticles and collective modes are two fundamental aspects that characterize quantum matter in addition to its ground-state features. For example, the low-energy physics for Fermi-liquid phase in He-III is featured not only by fermionic quasiparticles near the chemical potential but also by fruitful collective modes in the long-wave limit, including several different sound waves that can propagate through it under different circumstances. On the other hand, it is very difficult for sound waves to be carried by electron liquid in ordinary metals due to the fact that long-range Coulomb interaction among electrons will generate a plasmon gap for ordinary electron density oscillation and thus prohibits the propagation of sound waves through it. In the present paper, we propose a unique type of acoustic collective mode in Weyl semimetals under magnetic field called chiral zero sound. Chiral zero sound can be stabilized under the so-called “chiral limit,” where the intravalley scattering time is much shorter than the intervalley one and propagates only along an external magnetic field for Weyl semimetals with multiple pairs of Weyl points. The sound velocity of chiral zero sound is proportional to the field strength in the weak field limit, whereas it oscillates dramatically in the strong field limit, generating an entirely new mechanism for quantum oscillations through the dynamics of neutral bosonic excitation, which may manifest itself in the thermal conductivity measurements under magnetic field.

Spattering has been a problem in metal processing involving high-power lasers, like laser welding, machining, and recently, additive manufacturing. Limited by the capabilities of in situ diagnostic techniques, typically imaging with visible light or laboratory x-ray sources, a comprehensive understanding of the laser-spattering phenomenon, particularly the extremely fast spatters, has not been achieved yet. Here, using MHz single-pulse synchrotron-x-ray imaging, we probe the spattering behavior of Ti-6Al-4V with micrometer spatial resolution and subnanosecond temporal resolution. Combining direct experimental observations, quantitative image analysis, as well as numerical simulations, our study unravels a novel mechanism of laser spattering: The bulk explosion of a tonguelike protrusion forming on the front keyhole wall leads to the ligamentation of molten metal at the keyhole rims and the subsequent spattering. Our study confirms the critical role of melt and vapor flow in the laser-spattering process and opens a door to manufacturing spatter- and defect-free metal parts via precise control of keyhole dynamics.

Since its introduction by Berry in 1984, the geometric phase has become of fundamental importance in physics, with applications ranging from solid-state physics to optics. In optics, the Pancharatnam-Berry phase allows the tailoring of optical beams by a local control of their polarization. Here, we discuss light propagation in the presence of an intensity-dependent local modulation of the Pancharatnam-Berry phase. The corresponding self-modulation of the wave front counteracts the natural spreading due to diffraction; i.e., self-focusing takes place. No refractive index variation is associated with the self-focusing: The confinement is uniquely due to a nonlinear spin-orbit interaction. The phenomenon is investigated, both theoretically and experimentally, by considering the reorientational nonlinearity in liquid crystals, where light is able to rotate the local optical axis through an intensity-dependent optical torque. Our discoveries pave the way to the investigation of a new family of nonlinear waves featuring a strong interaction between the spin and the orbital degrees of freedom.

Density-functional perturbation theory (DFPT) is nowadays the method of choice for the accurate computation of linear and nonlinear-response properties of materials from first principles. A notable advantage of DFPT over alternative approaches is the possibility of treating incommensurate lattice distortions with an arbitrary wave vector $\mathbf{q}$ at essentially the same computational cost as the lattice-periodic case. Here we show that $\mathbf{q}$ can be formally treated as a perturbation parameter and used in conjunction with the established results of perturbation theory (e.g., the “$2n+1$” theorem) to perform a long-wave expansion of an arbitrary response function in powers of the wave-vector components. This procedure provides a powerful general framework to access a wide range of spatial dispersion effects that were formerly difficult to calculate by means of first-principles electronic structure methods. In particular, the physical response to the spatial gradient of any external field can now be calculated at negligible cost by using the response functions to uniform perturbations (electric, magnetic, or strain fields) as the only input. We demonstrate our method by calculating the flexoelectric and dynamical quadrupole tensors of selected crystalline insulators and model systems.

Modulating the frequency of a harmonic oscillator at nearly twice its natural frequency leads to amplification and self-oscillation. Above the oscillation threshold and in the presence of a nonlinearity, the field settles into a coherent oscillating state with a well-defined phase of either 0 or $\pi$. We demonstrate a quantum parametric oscillator operating at microwave frequencies and drive it into oscillating states containing only a few photons. The small number of photons present in the system and the coherent nature of the nonlinearity prevent the environment from learning the randomly chosen phase of the oscillator. This result allows the system to oscillate briefly in a quantum superposition of both phases at once, effectively generating a nonclassical Schrödinger’s cat state. We characterize the dynamics and states of the system by analyzing the output field emitted by the oscillator and implementing quantum state tomography suited for nonlinear resonators. By demonstrating a quantum parametric oscillator and the requisite techniques for characterizing its quantum state, we set the groundwork for new schemes of quantum and classical information processing and extend the reach of these ubiquitous devices deep into the quantum regime.

We explore the interplay of electron-electron correlations and spin-orbit coupling in the model Fermi liquid ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ using laser-based angle-resolved photoemission spectroscopy. Our precise measurement of the Fermi surface confirms the importance of spin-orbit coupling in this material and reveals that its effective value is enhanced by a factor of about 2, due to electronic correlations. The self-energies for the $\beta$ and $\gamma$ sheets are found to display significant angular dependence. By taking into account the multi-orbital composition of quasiparticle states, we determine self-energies associated with each orbital component directly from the experimental data. This analysis demonstrates that the perceived angular dependence does not imply momentum-dependent many-body effects but arises from a substantial orbital mixing induced by spin-orbit coupling. A comparison to single-site dynamical mean-field theory further supports the notion of dominantly local orbital self-energies and provides strong evidence for an electronic origin of the observed nonlinear frequency dependence of the self-energies, leading to “kinks” in the quasiparticle dispersion of ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$.

The properties of the isotropic incompressible $\nu =5/2$ fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform $p_x+i{p}_y$ pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at $\nu =5/2$. This finding motivates us to consider an inhomogeneous paired state—a $p_x+i{p}_y$ pair-density wave (PDW)—whose melting could be the origin of the observed liquid-crystalline phases. This state can viewed as an array of domain and antidomain walls of the $p_x+i{p}_y$ order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and antidomain walls) where the order parameter changes sign, support a pair of symmetry-protected counterpropagating Majorana modes. The coupling behavior of the domain-wall Majorana modes crucially depends on the interplay of the Fermi energy $E_F$ and the PDW pairing energy $E_{\mathrm{P}\mathrm{D}\mathrm{W}}$. The analysis of this interplay yields a rich set of topological states: (1) In the weak-coupling regime ($E_F>E_{\mathrm{P}\mathrm{D}\mathrm{W}}$), the hybridization of domain walls leads to a Majorana Fermi surface (MFS), which is protected by inversion and particle-hole symmetries. (2) As the MFS shrinks towards degenerate Dirac points, lattice effects render it unstable towards an Abelian stripe phase with two copropagating Majorana modes at the boundary. (3) A uniform component of the order parameter, which breaks inversion symmetry, gaps the MFS and causes the system to enter a non-Abelian FQH state supporting a chiral Majorana edge state. (4) In the strong-coupling regime, $E_F<E_{\mathrm{P}\mathrm{D}\mathrm{W}}$, the bulk fermionic spectrum becomes gapped; this is a trivial phase with no chiral Majorana edge states, which is in the universality class of an Abelian Halperin paired state. The pair-density-wave order state in a paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases—as well as transitions thereof—tuned by the strength of the paired liquid crystalline order.

With the help of quantum key distribution (QKD), two distant peers are able to share information-theoretical secure key bits. Increasing the key rate is ultimately significant for the applications of QKD in the lossy channel. However, it has been proven that there is a fundamental rate-distance limit, called the linear bound, which restricts the performance of all existing repeaterless protocols and realizations. Surprisingly, a recently proposed protocol, called twin-field (TF) QKD, can beat the linear bound with no need for quantum repeaters. Here, we present one of the first implementations of the TF-QKD protocol and demonstrate its advantage of beating the linear bound at a channel distance of 300 km. In our experiment, a modified TF-QKD protocol that does not assume phase postselection is considered, and thus a higher key rate than the original one is expected. After controlling the phase evolution of the twin fields traveling through hundreds of kilometers of optical fibers, the implemented system achieves high-visibility single-photon interference and allows stable and high-rate measurement-device-independent QKD. Our experimental demonstration and results confirm the feasibility of the TF-QKD protocol and its prominent superiority in long-distance key distribution services.

Gates in error-prone quantum information processors are often modeled using sets of one- and two-qubit process matrices, the standard model of quantum errors. However, the results of quantum circuits on real processors often depend on additional external “context” variables. Such contexts may include the state of a spectator qubit, the time of data collection, or the temperature of control electronics. In this article, we demonstrate a suite of simple, widely applicable, and statistically rigorous methods for detecting context dependence in quantum-circuit experiments. They can be used on any data that comprise two or more “pools” of measurement results obtained by repeating the same set of quantum circuits in different contexts. These tools may be integrated seamlessly into standard quantum device characterization techniques, like randomized benchmarking or tomography. We experimentally demonstrate these methods by detecting and quantifying crosstalk and drift on the publicly accessible 16-qubit ibmqx3.

The effects of uniaxial compressive stress on the normal state ${}^{17}\mathrm{O}$ nuclear-magnetic-resonance properties of the unconventional superconductor ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ are reported. The paramagnetic shifts of both planar and apical oxygen sites show pronounced anomalies near the nominal $\mathbf{a}$-axis strain ${ϵ}_{aa}\equiv {ϵ}_v$ that maximizes the superconducting transition temperature $T_c$. The spin susceptibility weakly increases on lowering the temperature below $T\simeq 10\mathrm{K}$, consistent with an enhanced density of states associated with passing the Fermi energy through a van Hove singularity. Although such a Lifshitz transition occurs in the $\gamma$ band formed by the Ru $d_{xy}$ states hybridized with in-plane O $p_{\pi }$ orbitals, the large Hund’s coupling renormalizes the uniform spin susceptibility, which, in turn, affects the hyperfine fields of all nuclei. We estimate this “Stoner” renormalization $S$ by combining the data with first-principles calculations and conclude that this is an important part of the strain effect, with implications for superconductivity.